Polytope of Type {4,12,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,12,6}*1152e
if this polytope has a name.
Group : SmallGroup(1152,157549)
Rank : 4
Schlafli Type : {4,12,6}
Number of vertices, edges, etc : 8, 48, 72, 6
Order of s0s1s2s3 : 12
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {4,12,6}*576d, {4,12,6}*576f, {4,6,6}*576a
3-fold quotients : {4,12,2}*384b
4-fold quotients : {2,12,6}*288a, {4,6,6}*288d
6-fold quotients : {4,12,2}*192b, {4,12,2}*192c, {4,6,2}*192
8-fold quotients : {2,6,6}*144a
12-fold quotients : {2,12,2}*96, {2,4,6}*96a, {4,3,2}*96, {4,6,2}*96b, {4,6,2}*96c
24-fold quotients : {4,3,2}*48, {2,2,6}*48, {2,6,2}*48
36-fold quotients : {2,4,2}*32
48-fold quotients : {2,2,3}*24, {2,3,2}*24
72-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,147)( 2,148)( 3,145)( 4,146)( 5,151)( 6,152)( 7,149)( 8,150)
( 9,155)( 10,156)( 11,153)( 12,154)( 13,159)( 14,160)( 15,157)( 16,158)
( 17,163)( 18,164)( 19,161)( 20,162)( 21,167)( 22,168)( 23,165)( 24,166)
( 25,171)( 26,172)( 27,169)( 28,170)( 29,175)( 30,176)( 31,173)( 32,174)
( 33,179)( 34,180)( 35,177)( 36,178)( 37,183)( 38,184)( 39,181)( 40,182)
( 41,187)( 42,188)( 43,185)( 44,186)( 45,191)( 46,192)( 47,189)( 48,190)
( 49,195)( 50,196)( 51,193)( 52,194)( 53,199)( 54,200)( 55,197)( 56,198)
( 57,203)( 58,204)( 59,201)( 60,202)( 61,207)( 62,208)( 63,205)( 64,206)
( 65,211)( 66,212)( 67,209)( 68,210)( 69,215)( 70,216)( 71,213)( 72,214)
( 73,219)( 74,220)( 75,217)( 76,218)( 77,223)( 78,224)( 79,221)( 80,222)
( 81,227)( 82,228)( 83,225)( 84,226)( 85,231)( 86,232)( 87,229)( 88,230)
( 89,235)( 90,236)( 91,233)( 92,234)( 93,239)( 94,240)( 95,237)( 96,238)
( 97,243)( 98,244)( 99,241)(100,242)(101,247)(102,248)(103,245)(104,246)
(105,251)(106,252)(107,249)(108,250)(109,255)(110,256)(111,253)(112,254)
(113,259)(114,260)(115,257)(116,258)(117,263)(118,264)(119,261)(120,262)
(121,267)(122,268)(123,265)(124,266)(125,271)(126,272)(127,269)(128,270)
(129,275)(130,276)(131,273)(132,274)(133,279)(134,280)(135,277)(136,278)
(137,283)(138,284)(139,281)(140,282)(141,287)(142,288)(143,285)(144,286);;
s1 := ( 3, 4)( 7, 8)( 11, 12)( 13, 25)( 14, 26)( 15, 28)( 16, 27)( 17, 29)
( 18, 30)( 19, 32)( 20, 31)( 21, 33)( 22, 34)( 23, 36)( 24, 35)( 39, 40)
( 43, 44)( 47, 48)( 49, 61)( 50, 62)( 51, 64)( 52, 63)( 53, 65)( 54, 66)
( 55, 68)( 56, 67)( 57, 69)( 58, 70)( 59, 72)( 60, 71)( 73,109)( 74,110)
( 75,112)( 76,111)( 77,113)( 78,114)( 79,116)( 80,115)( 81,117)( 82,118)
( 83,120)( 84,119)( 85,133)( 86,134)( 87,136)( 88,135)( 89,137)( 90,138)
( 91,140)( 92,139)( 93,141)( 94,142)( 95,144)( 96,143)( 97,121)( 98,122)
( 99,124)(100,123)(101,125)(102,126)(103,128)(104,127)(105,129)(106,130)
(107,132)(108,131)(147,148)(151,152)(155,156)(157,169)(158,170)(159,172)
(160,171)(161,173)(162,174)(163,176)(164,175)(165,177)(166,178)(167,180)
(168,179)(183,184)(187,188)(191,192)(193,205)(194,206)(195,208)(196,207)
(197,209)(198,210)(199,212)(200,211)(201,213)(202,214)(203,216)(204,215)
(217,253)(218,254)(219,256)(220,255)(221,257)(222,258)(223,260)(224,259)
(225,261)(226,262)(227,264)(228,263)(229,277)(230,278)(231,280)(232,279)
(233,281)(234,282)(235,284)(236,283)(237,285)(238,286)(239,288)(240,287)
(241,265)(242,266)(243,268)(244,267)(245,269)(246,270)(247,272)(248,271)
(249,273)(250,274)(251,276)(252,275);;
s2 := ( 1, 85)( 2, 88)( 3, 87)( 4, 86)( 5, 93)( 6, 96)( 7, 95)( 8, 94)
( 9, 89)( 10, 92)( 11, 91)( 12, 90)( 13, 73)( 14, 76)( 15, 75)( 16, 74)
( 17, 81)( 18, 84)( 19, 83)( 20, 82)( 21, 77)( 22, 80)( 23, 79)( 24, 78)
( 25, 97)( 26,100)( 27, 99)( 28, 98)( 29,105)( 30,108)( 31,107)( 32,106)
( 33,101)( 34,104)( 35,103)( 36,102)( 37,121)( 38,124)( 39,123)( 40,122)
( 41,129)( 42,132)( 43,131)( 44,130)( 45,125)( 46,128)( 47,127)( 48,126)
( 49,109)( 50,112)( 51,111)( 52,110)( 53,117)( 54,120)( 55,119)( 56,118)
( 57,113)( 58,116)( 59,115)( 60,114)( 61,133)( 62,136)( 63,135)( 64,134)
( 65,141)( 66,144)( 67,143)( 68,142)( 69,137)( 70,140)( 71,139)( 72,138)
(145,229)(146,232)(147,231)(148,230)(149,237)(150,240)(151,239)(152,238)
(153,233)(154,236)(155,235)(156,234)(157,217)(158,220)(159,219)(160,218)
(161,225)(162,228)(163,227)(164,226)(165,221)(166,224)(167,223)(168,222)
(169,241)(170,244)(171,243)(172,242)(173,249)(174,252)(175,251)(176,250)
(177,245)(178,248)(179,247)(180,246)(181,265)(182,268)(183,267)(184,266)
(185,273)(186,276)(187,275)(188,274)(189,269)(190,272)(191,271)(192,270)
(193,253)(194,256)(195,255)(196,254)(197,261)(198,264)(199,263)(200,262)
(201,257)(202,260)(203,259)(204,258)(205,277)(206,280)(207,279)(208,278)
(209,285)(210,288)(211,287)(212,286)(213,281)(214,284)(215,283)(216,282);;
s3 := ( 1, 5)( 2, 6)( 3, 7)( 4, 8)( 13, 17)( 14, 18)( 15, 19)( 16, 20)
( 25, 29)( 26, 30)( 27, 31)( 28, 32)( 37, 41)( 38, 42)( 39, 43)( 40, 44)
( 49, 53)( 50, 54)( 51, 55)( 52, 56)( 61, 65)( 62, 66)( 63, 67)( 64, 68)
( 73, 77)( 74, 78)( 75, 79)( 76, 80)( 85, 89)( 86, 90)( 87, 91)( 88, 92)
( 97,101)( 98,102)( 99,103)(100,104)(109,113)(110,114)(111,115)(112,116)
(121,125)(122,126)(123,127)(124,128)(133,137)(134,138)(135,139)(136,140)
(145,149)(146,150)(147,151)(148,152)(157,161)(158,162)(159,163)(160,164)
(169,173)(170,174)(171,175)(172,176)(181,185)(182,186)(183,187)(184,188)
(193,197)(194,198)(195,199)(196,200)(205,209)(206,210)(207,211)(208,212)
(217,221)(218,222)(219,223)(220,224)(229,233)(230,234)(231,235)(232,236)
(241,245)(242,246)(243,247)(244,248)(253,257)(254,258)(255,259)(256,260)
(265,269)(266,270)(267,271)(268,272)(277,281)(278,282)(279,283)(280,284);;
poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s3*s2*s1*s2*s3*s2, s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(288)!( 1,147)( 2,148)( 3,145)( 4,146)( 5,151)( 6,152)( 7,149)
( 8,150)( 9,155)( 10,156)( 11,153)( 12,154)( 13,159)( 14,160)( 15,157)
( 16,158)( 17,163)( 18,164)( 19,161)( 20,162)( 21,167)( 22,168)( 23,165)
( 24,166)( 25,171)( 26,172)( 27,169)( 28,170)( 29,175)( 30,176)( 31,173)
( 32,174)( 33,179)( 34,180)( 35,177)( 36,178)( 37,183)( 38,184)( 39,181)
( 40,182)( 41,187)( 42,188)( 43,185)( 44,186)( 45,191)( 46,192)( 47,189)
( 48,190)( 49,195)( 50,196)( 51,193)( 52,194)( 53,199)( 54,200)( 55,197)
( 56,198)( 57,203)( 58,204)( 59,201)( 60,202)( 61,207)( 62,208)( 63,205)
( 64,206)( 65,211)( 66,212)( 67,209)( 68,210)( 69,215)( 70,216)( 71,213)
( 72,214)( 73,219)( 74,220)( 75,217)( 76,218)( 77,223)( 78,224)( 79,221)
( 80,222)( 81,227)( 82,228)( 83,225)( 84,226)( 85,231)( 86,232)( 87,229)
( 88,230)( 89,235)( 90,236)( 91,233)( 92,234)( 93,239)( 94,240)( 95,237)
( 96,238)( 97,243)( 98,244)( 99,241)(100,242)(101,247)(102,248)(103,245)
(104,246)(105,251)(106,252)(107,249)(108,250)(109,255)(110,256)(111,253)
(112,254)(113,259)(114,260)(115,257)(116,258)(117,263)(118,264)(119,261)
(120,262)(121,267)(122,268)(123,265)(124,266)(125,271)(126,272)(127,269)
(128,270)(129,275)(130,276)(131,273)(132,274)(133,279)(134,280)(135,277)
(136,278)(137,283)(138,284)(139,281)(140,282)(141,287)(142,288)(143,285)
(144,286);
s1 := Sym(288)!( 3, 4)( 7, 8)( 11, 12)( 13, 25)( 14, 26)( 15, 28)( 16, 27)
( 17, 29)( 18, 30)( 19, 32)( 20, 31)( 21, 33)( 22, 34)( 23, 36)( 24, 35)
( 39, 40)( 43, 44)( 47, 48)( 49, 61)( 50, 62)( 51, 64)( 52, 63)( 53, 65)
( 54, 66)( 55, 68)( 56, 67)( 57, 69)( 58, 70)( 59, 72)( 60, 71)( 73,109)
( 74,110)( 75,112)( 76,111)( 77,113)( 78,114)( 79,116)( 80,115)( 81,117)
( 82,118)( 83,120)( 84,119)( 85,133)( 86,134)( 87,136)( 88,135)( 89,137)
( 90,138)( 91,140)( 92,139)( 93,141)( 94,142)( 95,144)( 96,143)( 97,121)
( 98,122)( 99,124)(100,123)(101,125)(102,126)(103,128)(104,127)(105,129)
(106,130)(107,132)(108,131)(147,148)(151,152)(155,156)(157,169)(158,170)
(159,172)(160,171)(161,173)(162,174)(163,176)(164,175)(165,177)(166,178)
(167,180)(168,179)(183,184)(187,188)(191,192)(193,205)(194,206)(195,208)
(196,207)(197,209)(198,210)(199,212)(200,211)(201,213)(202,214)(203,216)
(204,215)(217,253)(218,254)(219,256)(220,255)(221,257)(222,258)(223,260)
(224,259)(225,261)(226,262)(227,264)(228,263)(229,277)(230,278)(231,280)
(232,279)(233,281)(234,282)(235,284)(236,283)(237,285)(238,286)(239,288)
(240,287)(241,265)(242,266)(243,268)(244,267)(245,269)(246,270)(247,272)
(248,271)(249,273)(250,274)(251,276)(252,275);
s2 := Sym(288)!( 1, 85)( 2, 88)( 3, 87)( 4, 86)( 5, 93)( 6, 96)( 7, 95)
( 8, 94)( 9, 89)( 10, 92)( 11, 91)( 12, 90)( 13, 73)( 14, 76)( 15, 75)
( 16, 74)( 17, 81)( 18, 84)( 19, 83)( 20, 82)( 21, 77)( 22, 80)( 23, 79)
( 24, 78)( 25, 97)( 26,100)( 27, 99)( 28, 98)( 29,105)( 30,108)( 31,107)
( 32,106)( 33,101)( 34,104)( 35,103)( 36,102)( 37,121)( 38,124)( 39,123)
( 40,122)( 41,129)( 42,132)( 43,131)( 44,130)( 45,125)( 46,128)( 47,127)
( 48,126)( 49,109)( 50,112)( 51,111)( 52,110)( 53,117)( 54,120)( 55,119)
( 56,118)( 57,113)( 58,116)( 59,115)( 60,114)( 61,133)( 62,136)( 63,135)
( 64,134)( 65,141)( 66,144)( 67,143)( 68,142)( 69,137)( 70,140)( 71,139)
( 72,138)(145,229)(146,232)(147,231)(148,230)(149,237)(150,240)(151,239)
(152,238)(153,233)(154,236)(155,235)(156,234)(157,217)(158,220)(159,219)
(160,218)(161,225)(162,228)(163,227)(164,226)(165,221)(166,224)(167,223)
(168,222)(169,241)(170,244)(171,243)(172,242)(173,249)(174,252)(175,251)
(176,250)(177,245)(178,248)(179,247)(180,246)(181,265)(182,268)(183,267)
(184,266)(185,273)(186,276)(187,275)(188,274)(189,269)(190,272)(191,271)
(192,270)(193,253)(194,256)(195,255)(196,254)(197,261)(198,264)(199,263)
(200,262)(201,257)(202,260)(203,259)(204,258)(205,277)(206,280)(207,279)
(208,278)(209,285)(210,288)(211,287)(212,286)(213,281)(214,284)(215,283)
(216,282);
s3 := Sym(288)!( 1, 5)( 2, 6)( 3, 7)( 4, 8)( 13, 17)( 14, 18)( 15, 19)
( 16, 20)( 25, 29)( 26, 30)( 27, 31)( 28, 32)( 37, 41)( 38, 42)( 39, 43)
( 40, 44)( 49, 53)( 50, 54)( 51, 55)( 52, 56)( 61, 65)( 62, 66)( 63, 67)
( 64, 68)( 73, 77)( 74, 78)( 75, 79)( 76, 80)( 85, 89)( 86, 90)( 87, 91)
( 88, 92)( 97,101)( 98,102)( 99,103)(100,104)(109,113)(110,114)(111,115)
(112,116)(121,125)(122,126)(123,127)(124,128)(133,137)(134,138)(135,139)
(136,140)(145,149)(146,150)(147,151)(148,152)(157,161)(158,162)(159,163)
(160,164)(169,173)(170,174)(171,175)(172,176)(181,185)(182,186)(183,187)
(184,188)(193,197)(194,198)(195,199)(196,200)(205,209)(206,210)(207,211)
(208,212)(217,221)(218,222)(219,223)(220,224)(229,233)(230,234)(231,235)
(232,236)(241,245)(242,246)(243,247)(244,248)(253,257)(254,258)(255,259)
(256,260)(265,269)(266,270)(267,271)(268,272)(277,281)(278,282)(279,283)
(280,284);
poly := sub<Sym(288)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2,
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s1*s0*s1*s0*s1*s0*s1, s1*s2*s3*s2*s1*s2*s3*s2,
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope